It is necessary in a highly competitive marketplace to anticipate vibration problems on production machines before they introduce major product variations into a process or cause damage to production assets. Some speed relationships between interconnected rotating components, such as nipped rolls, pumps, and process webs, may result in patterns that cause uniformly spaced defects—referred to as bars or barring—in assets or products. The spacing or frequency of the barring is directly related to the rotational speed of the asset that caused the barring. Examples of possible asset barring sources include but are not limited to:                surfaces of rolls with soft covers being deformed into an integer number of evenly spaced ridges sometimes referred to as corrugations running primarily in the cross direction;        process webs, such as paper machine press felts, being deformed or worn into an integer spaced pattern that reflects the construction of the web, such as a lap joint deformation in the press felt of a paper machine; and        an upstream pump that provides product stock to a process introducing pump-related pulsations into the delivered product stock, such as pulsations at the pump running speed or pump blade pass pulsations. The frequency of these pulsations through the product stock can introduce vibration into a downstream rotating asset. If the pulsation frequency matches a speed or multiple of a speed of the downstream rotating asset, it causes the downstream asset to have enhanced vibration. This enhanced vibration can cause the downstream rotating asset to become unstable.        
All of these issues and others can result in damaged rotating assets and may also result in product barring that may make the finished product unsalable or salable only in a lower quality category.
Manually calculating ratiometric relationships between rotating assets is generally unreliable and usually involves using coarse data such as grind diameters of rolls and delivered lengths of felts, dividing the circumference of one component into the circumference of another component, and then determining whether the result or whole multiples thereof are close to being an integer amount. This calculation requires subjective assessment of the results to round off the numbers.
A major error in this method is that the asset diameters change when they are installed and running. One example is the compression of a soft roll when it is nipped to another roll in a paper machine press section. The unknown amount of compression causes the effective diameter of the roll to change, thereby nullifying the calculation result. When a paper machine felt is installed it is tensioned which stretches the felt and changes its circumference. In general, when assets are loaded and running, their diameters or circumferences change. Also, slippage can occur when the assets are not geared to each other. As a result, most rotating assets will not have predictable ratiometric relationships based on their static physical measurements. Another hindrance to calculating the ratios is the constant and sometimes asset-independent readjustment of process conditions such as process speed and other process settings.
Some vibration training courses have taught that if a low-order integer relationship exists in a gear set then the gears can experience a phenomenon called “hunting tooth.” This is a situation in which the gear teeth mesh in a frequently repeating pattern due an integer ratiometric relationship. This results in premature gear failure. This same issue occurs in non-geared rotating assets, but there has been no reliable method to predict this phenomenon.
There have been some prior efforts to use a factorial method of determining whether an integer ratio exists between rotating components, where the method is based on the physical diameters of the rotating assets. This method of using physical diameters is inaccurate for several reasons:                Factoring rational numbers is awkward and can lead to a presumption that multiple ratios exist when only one ratio actually exists.        When rolls are pressed together, their diameter changes which changes their ratiometric relationship, and there is no way to physically measure this change in diameter.        
This method is not applicable to rotating assets that have no measurable diameter, such as a pump. Although a pump impeller has a diameter, the pump impeller diameter has no meaning in ratiometric calculations. Only the pump running speed and blade pass frequency matter.                When rolls are pressed together they may have different surface speeds due to slippage between the surfaces. Thus, their speeds are not locked together based on a physical size in the same way that gears are locked by engaged teeth that do not permit slippage.Using any sort of physical sizing for ratio analysis except for gearing is an inaccurate method of determining possible integer ratiometric relationships and cannot be used in real time to determine the integer ratiometric relationships of a running machine.        
What is needed, therefore, is an improved method for determining ratiometric relationships of interrelated rotating assets.